HW 05 - Workflow for algorithms in time series modelling

Financial Time Series Forecasting Example

library(xgboost)
library(tidymodels)
library(modeltime)
library(tidyverse)
library(lubridate)
library(timetk)

# This toggles plots from plotly (interactive) to ggplot (static)
interactive <- TRUE

Step 1 - Collect data and split into training and test sets.

# Data
tidyquant::tq_get("^VIX",from="2020-01-01") %>% 
  select(date,adjusted) %>% 
  rename(value=adjusted)->vix

One poor quality feature of yahoo finance API data is that you can have potentially overlapping dates. This will create bias in any time series models so needs to be consider at this pre-processing stage.

Do we have duplicate dates?

vix[duplicated(vix$date,fromLast = T),]$date->duplicated_date
vix %>% filter(date==duplicated_date)
#> # A tibble: 2 × 2
#>   date       value
#>   <date>     <dbl>
#> 1 2022-03-18  23.9
#> 2 2022-03-18  23.9

vix<-vix %>% distinct(date,.keep_all = TRUE)

We can visualize the dataset.

vix %>%
  plot_time_series(date, value, .interactive = interactive)

Let’s split the data into training and test sets using initial_time_split()

# Split Data 80/20
splits <- initial_time_split(vix, prop = 0.8)

Step 2 - Create & Fit Multiple Models

We can easily create dozens of forecasting models by combining modeltime and parsnip. We can also use the workflows interface for adding preprocessing! Your forecasting possibilities are endless. Let’s get a few basic models developed:

Boosting, is one of many approach for improving the predictions from a prediction model. Like bagging, boosting is a general approach that can be applied to many statistical learning methods including time series models. Bagging involves creating multiple copies of the original training data set using the bootstrap, fitting a similar model to each copy, and then combining all of the model estimates in order to create a single predictive model. Notably, each model is built on a bootstrap data set, independent of the other models. Boosting works in a similar way, except that the models are grown sequentially: each model is grown using information from previously estimated models. Boosting does not involve bootstrap sampling; instead each tree is fit on a modified version of the original data set. In the following example we will simply use boosting to see if we can improve on ARIMA model errors (residuals). Boosting can also be applied to the predictors in the model

See section 8.3 in below. Download an second edition copy here

ARIMA
ARIMA boosted
Exponential Smoothing
Linear Regression
MARS (Multivariate Adaptive Regression Splines) a non-linear generalised additive model

Important note: Handling Date Features

Modeltime models (e.g. arima_reg()) are created with a date or date time feature in the model. You will see that most models include a formula like fit(value ~ date, data).

Parsnip models (e.g. linear_reg()) typically should not have date features, but may contain derivatives of dates (e.g. month, year, etc). You will often see formulas like fit(value ~ as.numeric(date) + month(date), data).

Model 1: Auto ARIMA (Modeltime)

First, we create a basic univariate ARIMA model using “Auto Arima” using arima_reg()

# Model 1: auto_arima ----
model_fit_arima_no_boost <- arima_reg() %>%
    set_engine(engine = "auto_arima") %>%
    fit(value ~ date, data = training(splits))
#> frequency = 5 observations per 1 week

Model 2: Boosted Auto ARIMA (Modeltime)

Next, we create a boosted ARIMA using arima_boost(). Boosting uses XGBoost to model the ARIMA errors. Note that model formula contains both a date feature and derivatives of date - ARIMA uses the date - XGBoost uses the derivatives of date as regressors

Normally I’d use a preprocessing workflow for the month features using a function like step_timeseries_signature() from timetk to help reduce the complexity of the parsnip formula interface.

# Model 2: arima_boost ----
model_fit_arima_boosted <- arima_boost(
    min_n = 2,
    learn_rate = 0.015
) %>%
    set_engine(engine = "auto_arima_xgboost") %>%
    fit(value ~ date + as.numeric(date) + 
          factor(month(date, label = TRUE), ordered = F),
        data = training(splits))
#> frequency = 5 observations per 1 week

Model 3: Exponential Smoothing (Modeltime)

Next, create an Error-Trend-Season (ETS) model using an Exponential Smoothing State Space model. This is accomplished with exp_smoothing().

# Model 3: ets ----
model_fit_ets <- exp_smoothing() %>%
    set_engine(engine = "ets") %>%
    fit(value ~ date, data = training(splits))
#> frequency = 5 observations per 1 week

Model 4: Prophet (Modeltime)

We’ll create a prophet model using prophet_reg().

# Model 4: prophet ----
model_fit_prophet <- prophet_reg() %>%
    set_engine(engine = "prophet") %>%
    fit(value ~ date, data = training(splits))
#> Disabling yearly seasonality. Run prophet with yearly.seasonality=TRUE to override this.
#> Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

Model 5: Linear Regression (Parsnip)

We can model time series linear regression (TSLM) using the linear_reg() algorithm from parsnip. The following derivatives of date are used:

Trend: Modeled using as.numeric(date)
Seasonal: Modeled using month(date)

# Model 5: lm ----
model_fit_lm <- linear_reg() %>%
    set_engine("lm") %>%
    fit(value ~ as.numeric(date) + 
          factor(month(date, label = TRUE), ordered = FALSE),
        data = training(splits))

Model 6: MARS (Workflow)

We can model a Multivariate Adaptive Regression Spline model using mars(). I’ve modified the process to use a workflow to standardize the preprocessing of the features that are provided to the machine learning model (mars).

# Model 6: earth ----
model_spec_mars <- mars(mode = "regression") %>%
    set_engine("earth") 

recipe_spec <- recipe(value ~ date, data = training(splits)) %>%
    step_date(date, features = "month", ordinal = FALSE) %>%
    step_mutate(date_num = as.numeric(date)) %>%
    step_normalize(date_num) %>%
    step_rm(date)
  
wflw_fit_mars <- workflow() %>%
    add_recipe(recipe_spec) %>%
    add_model(model_spec_mars) %>%
    fit(training(splits))

OK, with these 6 models, we’ll show how easy it is to forecast.

Step 3 - Add fitted models to a Model Table.

The next step is to add each of the models to a Modeltime Table using modeltime_table(). This step does some basic checking to make sure each of the models are fitted and that organizes into a scalable structure called a “Modeltime Table” that is used as part of our forecasting workflow.

We have 6 models to add. A couple of notes before moving on:

Note that some of the models have tunable parameters.
It’s expected that tuning and parameter selection is performed prior to incorporating into a Modeltime Table.
If you try to add an unfitted model, the modeltime_table() will complain (throw an informative error) saying you need to fit() the model.

models_tbl <- modeltime_table(
    model_fit_arima_no_boost,
    model_fit_arima_boosted,
    model_fit_ets,
    model_fit_prophet,
    model_fit_lm,
    wflw_fit_mars
)

models_tbl
#> # Modeltime Table
#> # A tibble: 6 × 3
#>   .model_id .model     .model_desc                   
#>       <int> <list>     <chr>                         
#> 1         1 <fit[+]>   ARIMA(1,1,4)                  
#> 2         2 <fit[+]>   ARIMA(1,1,4) W/ XGBOOST ERRORS
#> 3         3 <fit[+]>   ETS(M,A,N)                    
#> 4         4 <fit[+]>   PROPHET                       
#> 5         5 <fit[+]>   LM                            
#> 6         6 <workflow> EARTH

Step 4 - Calibrate the model to a testing set.

Calibrating adds a new column, .calibration_data, with the test predictions and residuals inside. A few notes on Calibration:

Calibration is how confidence intervals and accuracy metrics are determined
Calibration Data is simply forecasting predictions and residuals that are calculated from out-of-sample data.
After calibrating, the calibration data follows the data through the forecasting workflow.

calibration_tbl <- models_tbl %>%
    modeltime_calibrate(new_data = testing(splits))

calibration_tbl
#> # Modeltime Table
#> # A tibble: 6 × 5
#>   .model_id .model     .model_desc                    .type .calibration_data 
#>       <int> <list>     <chr>                          <chr> <list>            
#> 1         1 <fit[+]>   ARIMA(1,1,4)                   Test  <tibble [112 × 4]>
#> 2         2 <fit[+]>   ARIMA(1,1,4) W/ XGBOOST ERRORS Test  <tibble [112 × 4]>
#> 3         3 <fit[+]>   ETS(M,A,N)                     Test  <tibble [112 × 4]>
#> 4         4 <fit[+]>   PROPHET                        Test  <tibble [112 × 4]>
#> 5         5 <fit[+]>   LM                             Test  <tibble [112 × 4]>
#> 6         6 <workflow> EARTH                          Test  <tibble [112 × 4]>

Step 5 - Testing Set Forecast & Accuracy Evaluation

There are 2 critical parts to an evaluation.

Visualizing the Forecast vs Test Data Set
Evaluating the Test (Out of Sample) Accuracy

5A - Visualizing the Forecast Test

Visualizing the Test Error is easy to do using the interactive plotly visualization (just toggle the visibility of the models using the Legend).

calibration_tbl %>%
    modeltime_forecast(
        new_data    = testing(splits),
        actual_data = vix
    ) %>%
    plot_modeltime_forecast(
      .legend_max_width = 25, # For mobile screens
      .interactive      = interactive
    )

Describe the output

5B - Accuracy Metrics

We can use modeltime_accuracy() to collect common accuracy metrics. The default reports the following metrics using yardstick functions:

MAE - Mean absolute error, mae()
MAPE - Mean absolute percentage error, mape()
MASE - Mean absolute scaled error, mase()
SMAPE - Symmetric mean absolute percentage error, smape()
RMSE - Root mean squared error, rmse()
RSQ - R-squared, rsq()

These of course can be customized following the rules for creating new yardstick metrics, but the defaults are very useful. Refer to default_forecast_accuracy_metrics() to learn more.

To make table-creation a bit easier, I’ve included table_modeltime_accuracy() for outputing results in either interactive (reactable) or static (gt) tables.

calibration_tbl %>%
    modeltime_accuracy() %>%
    table_modeltime_accuracy(
        .interactive = interactive
    )